Modules which are invariant under idempotents of their envelopes

Thuyet, Le Van; Dan, Phan; Quynh, Truong Cong

doi:10.4064/cm6496-1-2016

Cited by 2 publications

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“…It is well known that a module M is quasiinjective if and only if f (M ) ≤ M for any endomorphism f of the injective envelope of the module M (see [7]). A module M is said to be automorphism-invariant if f (M ) ≤ M for any automorphism f of the injective envelope of M. Automorphisminvariant modules are studied in [4], [6], [17], [21], and [22].…”

Section: Introductionmentioning

confidence: 99%

On Automorphism-invariant multiplication modules over a noncommutative ring

Thuyet,

Quynh

2024

International Electronic Journal of Algebra

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One of the important classes of modules is the class of multiplication modules over a commutative ring. This topic has been considered by many authors and numerous results have been obtained in this area. After that, Tuganbaev also considered the multiplication module over a noncommutative ring. In this paper, we continue to consider the automorphism-invariance of multiplication modules over a noncommutative ring. We prove that if $R$ is a right duo ring and $M$ is a multiplication, finitely generated right $R$-module with a generating set $\{m_1, \dots , m_n\}$ such that $r(m_i) = 0$ and $[m_iR: M] \subseteq C(R)$ the center of $R$, then $M$ is projective. Moreover, if $R$ is a right duo, left quasi-duo, CMI ring and $M$ is a multiplication, non-singular, automorphism-invariant, finitely generated right $R$-module with a generating set $\{m_1, \dots , m_n\}$ such that $r(m_i) = 0$ and $[m_iR: M] \subseteq C(R)$ the center of $R$, then $M_R \cong R$ is injective.

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Section: Introductionmentioning

confidence: 99%

On Automorphism-invariant multiplication modules over a noncommutative ring

Thuyet,

Quynh

2024

International Electronic Journal of Algebra

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“…Общая теория модулей, инвариантных и коинвариантных относительно автоморфизмов соответственно своей оболочки и своего накрытия, была в последнее время развита в [20][21][22]. Теория модулей, инвариантных относительно идемпотентных эндморфизмов своей оболочки, изучена в [23].…”

Section: Introductionunclassified

Модули, Коинвариантные Относительно Идемпотентных Эндоморфизмов Своих Накрытий

Abyzov¹,

Le²,

Truong³

et al. 2019

Sib. Mat. Zh.

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Аннотация. Изучаются модули, коинвариантные относительно идемпотентных эндоморфизмов своих накрытий. Вводятся и изучаются обобщения дискретных и непрерывных модулей с помощью теории накрытий и оболочек модулей. В качестве приложения рассмотрены случаи плоских накрытий, инъективных оболочек и чисто инъективных оболочек.

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Modules which are invariant under idempotents of their envelopes

Cited by 2 publications

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On Automorphism-invariant multiplication modules over a noncommutative ring

On Automorphism-invariant multiplication modules over a noncommutative ring

Модули, Коинвариантные Относительно Идемпотентных Эндоморфизмов Своих Накрытий

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